Corrigendum to “Sharkovskii theorem for infinite dimensional dynamical systems” [Communications in Nonlinear Science and Numerical Simulation 146 (2025) 108770

In the space of system parameters, the closedform stability chart is determined for the delayed Mathieu equation defined as (t)(cost)x(t) bx(t2). This stability chart makes the connection between t...

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for a nonlinear m-point boundary value problem for the following second-order dynamic equation on time scales $$\begin{array}{l}(\phi(u^{\Delta}))^{\nabla}+a(t)f(t,u(t))=0,\quad t\in(0,T),\\\noalign{\vspace{2mm}}\displaystyle u(0)=\sum_{i=1}^{m-2}a_{i}u(\xi_{i}),\qquad \phi(u^{\Delta}(T))=\sum_{i=1}^{m-2}b_{i}\phi(u^{\Delta}(\xi_{i})),\end{array}$$ where φ:R⟶R is an increasing homeomorphism and positive homomorphism with φ(0)=0. The nonlinear term f may change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. We should point out that the above equation we studied is same as that in Han and Jin (Communications in Nonlinear Science and Numerical Simulation, 2009), but the methods is different from Han and Jin (Communications in Nonlinear Science and Numerical Simulation, 2009), we generalize and improve the results (Han and Jin, Communications in Nonlinear Science and Numerical Simulation, 2009). As an application, a typical example to demonstrate our results is given.

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.

In this article, dynamics and stability of milling operations with cylindrical end mills are investigated. A unified–mechanics–based model, which allows for both regenerative effects and loss–of–contact effects, is presented for study of partial–immersion, high–immersion and slotting operations. Reduced–order models that can be used for certain milling operations such as full–immersion operations and finishing cuts are also presented. On the basis of these models, the loss of stability of periodic motions of the workpiece–tool system is assessed by using Poincare sections and the numerical predictions of stable and unstable motions are found to correlate well with the corresponding experimental observations. Bifurcations experienced by periodic motions of the workpiece–tool system with respect to quasi–static variation of parameters such as axial depth of cut are examined and discussed. For partial–immersion operations, consideration of both time–delay effects and loss–of–contact effects is shown to have a significant influence on the structure of the stability boundaries in the space of spindle speed and axial depth of cut. The sensitivity of system dynamics to multiple–regenerative effects, mode–coupling effects and feed rate is also discussed.

This data article comprises data to investigate the non-linear dynamic behavior of the CEA-beam benchmark structure subjected to one stochastic broadband excitation. Experiments have been performed on the CEA-CESTA laboratory. The data provided include the input Power Spectral Density for four levels of excitation and the associated output nonlinear dynamic behavior of the CEA-beam benchmark structure. All the results from this data will help researchers and engineers in proper analysis of hardening effect and the enlargement of the response peak due to one stochastic broadband excitation, as well as the presence of harmonics. One of the main original contributions is to share the data sets to give the opportunity to researchers for testing and validating analytical or numerical models of a nonlinear beam with non-ideal boundary conditions and subjected to one stochastic broadband excitation. This Data in Brief article is an additional item directly alongside the following paper published in the Communications in Nonlinear Science and Numerical Simulation (CNSNS) journal: T. Roncen, J-P. Lambelin and J-J. Sinou, Nonlinear vibrations of a beam with non-ideal boundary conditions and stochastic excitations - experiments, modeling and simulations, Communications in Nonlinear Science and Numerical Simulation,74 (2019) 14-29. doi.org/10.1016/j.cnsns.2019.03.006

Dataset of multi-harmonic measurements for the experimental CEA-beam benchmark structure

In this paper, we analyse mixing in an active chaotic advection micromixer. The micromixer consists of a main rectangular channel and three cross-stream secondary channels that provide ability for time-dependent actuation of the flow stream in the direction orthogonal to the main stream. Three-dimensional motion in the mixer is studied. Numerical simulations and modelling of the flow are pursued in order to understand the experiments. It is shown that for some values of parameters a simple model can be derived that clearly represents the flow nature. Particle image velocimetry measurements of the flow are compared with numerical simulations and the analytical model. A measure for mixing, the mixing variance coefficient (MVC), is analysed. It is shown that mixing is substantially improved with multiple side channels with oscillatory flows, whose frequencies are increasing downstream. The optimization of MVC results for single side-channel mixing is presented. It is shown that dependence of MVC on frequency is not monotone, and a local minimum is found. Residence time distributions derived from the analytical model are analysed. It is shown that, while the average Lagrangian velocity profile is flattened over the steady flow, Taylor-dispersion effects are still present for the current micromixer configuration.

In this paper we extend our recently developed theory of absolute instability of spatially developing localized open flows and media to treating the case when the physical properties of the base state tend algebraically to constant properties at ±∞. The Laplace–transformed problem Z x ( x , ω ) = [ A ( ω ) + ( x ) ] Z ( x , ω ) + g ( x , ω ) , governing the perturbation dynamics of the flow is treated as a dynamical system. Here, Z ( x, ω ) is the Laplace–transformed perturbation, x e R is the spatial coordinate, ω e C is a frequency (and a Laplace transform parameter) and g( x, ω ) is the source function. The analysis assumes that the entries of the tail matrix R ( x ) decay as | x |– α , when x → ± ∞, where α > 0 is sufficiently large. We impose no restriction on the rate of variability of R ( x ) in the finite domain. The Levinson theorem is used for obtaining decompositions of the fundamental matrix of the system, Φ ( x , ω ) = B ± ( x , ω ) e A ( ω ) x [ B ± ( 0 , ω ) ] - 1 with the asymptotics B±( x, ω ) = I + 0 |x|− ϵ), ϵ > 0, when x → ± ∞ , respectively, where I is the identity matrix, which parallel the Floquet decomposition in the spatially periodic case. By using these decompositions, the boundary conditions of decay of Z ( x, ω ), when x → ±∞, are formulated in terms of B ±( x,ω ) and of two projectors on the subspaces spanned by the eigenvectors and generalized eigenvectors of A ( ω ) having the eigenvalues with positive and, correspondingly, negative real parts. The boundary–value problem for Z ( x, ω ) is solved formally, and the dispersion relation functions, Dn ( ω ), for the global normal modes, for the corresponding regions, R n ⊂ C, n ⩾ 1, are expressed in terms of the projectors and the matrices B ±(0, ω ). When the associated uniform state, i.e. the one with R ( x ) being zero, is stable, the flow is shown to be globally unstable if and only if the function D 1( ω ) has a root in the upper ω –half–plane. A formal solution of the initial–value linear stability problem is obtained, and it is shown that the flow is absolutely unstable if and only if either the analytic continuation, D∼ 1( ω ), of D 1( ω ) has a root or one of the matrix functions B ±(0, ω ) has a singularity, for ω with Im ω > 0, or the associated uniform flow is absolutely unstable or a combination of the above holds. It is argued that the concept of local stability cannot be consistently defined for open inhomogeneous flows treated. We present a procedure for analysing a spatially developing open flow on global and absolute instabilities, and suggest a frequency–selection criterion for open flows with self–sustained oscillations.

The biphasic decay of blood viraemia in patients being treated for human immunodeficiency virus type 1 (HIV-1) infection has been explained as the decay of two distinct populations of cells: the rapid death of productively infected cells followed by the much slower elimination of a second population the identity of which remains unknown. Here we advance an alternative explanation based on the immune response against a single population of infected cells. We show that the biphasic decay can be explained simply, without invoking multiple compartments: viral load falls quickly while cytotoxic T lymphocytes (CTL) are still abundant, and more slowly as CTL disappear. We propose a method to test this idea, and develop a framework that is readily applicable to treatment of other infections.

Corrigendum to “Dynamical systems method for solving operator equations” [Communications in Nonlinear Science and Numerical Simulation 9 (2004)

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.

Stud krill herd algorithm

Corrigendum to “Early warning detection of runaway initiation using non-linear approaches” [Communications in Nonlinear Science and Numerical Simulation 9 (2004)

Corrigendum to “The impacts of the individual activity and attractiveness correlation on spreading dynamics in time-varying networks” [Communications in Nonlinear Science and Numerical Simulation, Volume 122, July 2023, 107233]

Comment on: Multi soliton solution, rational solution of the Boussinesq–Burgers equations